Design of arbitrarily directional cloaks by solving the Laplace’s equation

Abstract

Articles you may be interested inDesigning a square invisibility cloak using metamaterials made of stacked positive-negative index slabs Design of optical cloaks and illusion devices along a circumferential direction in curvilinear coordinatesWe propose a robust method to design arbitrarily directional cloaks by solving the Laplace's equation. The method is based on the orthogonality between light rays and eikonal curves. By employing the analogy between light rays and electric force lines, and the equivalence between eikonal curves and isopotential lines, the original problem in the geometrical optics is converted into a boundary value problem in electrostatics. Examples are given and the simulation results validate the design. The method can also be used to design other optical-transformation devices and be extended to solve three-dimensional problems. The medium parameters designed by the method are easily realized using metamaterials or normal materials, and hence, the method can find applications in the optical and microwave engineering.

An analogy strategy for transformation optics

“…For devices performing a unidirectional behavior, the analogy idea bridges the transformation approach and ray optics formulae to create feasible 3D profiles, which are hardly achievable using either technique alone. Although the examples shown here are isotropic, some of which can be obtained as well by solving Laplaceʼs equation [38,63], we believe it is possible to find analogies to anisotropic systems for biaxial [64] or more advanced devices [65]. Meanwhile, numerical techniques should not be excluded for complex geometries.…”

A multidirectional cloak for visible light

“…Likewise, conformal transformation also shows great advantages in easing the material properties since the materials it results in are isotropic [1,13,14]. Subsequently, plasmonic resonances [15], metasurfaces [16,17], analogies to eikonal equations [18][19][20], and topology optimization [21], etc, were also proposed to enrich the cloaking strategies. Furthermore, conventional optical lens fabrication was incorporated into a transformation principle by applying calcite [22,23], a kind of natural anisotropic optical material, to eliminate the process of complicated nano-or microfabrication that the previous cloaks required [10][11][12]16], through which macroscopic cloaks were demonstrated at polarized light.…”

Horizontal cloaking and vertical reflection by transformation acoustics

“…Mei et al 18 and Vasic et al 19 made use of inhomogeneous isotropic materials by changing the refractive index distributions. These devices allow an object to be cloaked from waves in certain directions.…”